How can I rotate multiple objects in their LOCAL axis?
There's a simple method for that in Blender.Here The couple of Cubes represent your Multiple Objects.


Select one of the  object in your scene. (The nearby objects to the selection will have more influence of Random Rotation).

Change the Pivot Point to Individual.(So cubes will be rotated on their Local Axis)

Press 'O' in keyboard (To turn on Proportional Editing) &amp; set it to Random.



More Info while pressing R for rotate a circle will appear that represents the effective Radius for the Random Rotation that can be changed by (Mouse Wheel) or (Page Up or Page Down)